Answer:
[tex]h(x) = \frac{1}{4} x[/tex]
Step-by-step explanation:
To find the inverse of a function, the steps are:
Let y= f(x)Make x the subject of formulaReplace x with f⁻¹(x) and y with xIn this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.
_____
f(x)= 4x
Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]
y= 4x
Divide both sides by 4:
[tex] \frac{1}{4} y = x[/tex]
[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]
Replace x with h(x) and y with x:
[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]
Additional:
For a similar question on inverse functions, do check out the following!
https://brainly.com/question/21287415) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
Answer:
28 students
Step-by-step explanation:
7 times 4 = 28
there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class
Answer:
28
Keyword(s):
divided, four, 7, per team, how many
Step-by-step explanation:
7 × 4 = 28
Question 1 of 10
The slope of the line below is - Write a point-slope equation of the line -1/7
using the coordinates of the labeled point.
10
610
(3, 3)
10
610
Step-by-step explanation:
What is x in the figure?
im not sure I'd need to see the figure
8- Determine the midpoint of a line segment with the endpoints (8, 0) and
(4,6)
A. (3,6)
B. (7,3)
C. (6,3)
D. (7.6)
Can someone help pls ?
Answer:
C. (6, 3)
Step-by-step explanation:
Use the midpoint formula!
Midpoint Formula
[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
x₁, x₂ ... x-coordinates of the endpoints
y₁, y₂ ... y-coordinates of the endpoints
Given endpoints:
(8, 0)
(4, 6)
Points are in form (x, y).
Now let's substitute the variables in the formula with our values.
[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]
[tex](\frac{12}{2}, \frac{6}{2})[/tex]
[tex](6, 3)[/tex]
(6, 3) is our midpoint!
Question in the picture 1-5
how to understand next steps what will be anyone give me explains
Step-by-step explanation:
remember a few things :
a × -1 = -a
-a × -1 = a
-1 × -1 = 1
1 × a = a
therefore,
-1 × -1 × a = 1 × a = a
and finally
c × (a + b) = c×a + c×b
so, we can say
(1 - 5) = -1 × -1 × (1 - 5) =
= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =
= -1 × (5 - 1) = -(5 - 1)
The demand function for a christmas music cd is given by q=0. 6(3800-p^2)
The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a demand function:
q=0. 6(3800-p²)
Differentiate with respect to p:
[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]
We know the elasticity:
[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]
[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]
[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]
Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.
Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
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please help with math
I NEED HELP ASAPPPPPP
Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
Considering the given quadratic equation, the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the equation is given by:
h(t) = -(t - 12)² - 81.
The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
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What is the value of x?
(Round your answer to
the nearest tenth.)
Answer:
x ≈ 8.7
Step-by-step explanation:
given 2 secants from an external point to the circle, then
the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is
6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides
36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )
6x = 52 (divide both sides by 6 )
x ≈ 8.7 ( to the nearest tenth )
Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.
The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have three linear equations in three variables:
x - y - z = 0 ..(1)
2x - y + 2z = 1 ..(2)
x - y + z = -2 ..(3)
From the equation (1):
[tex]\rm x=y+z[/tex]
Plug this value in the equation (2) and (3):
[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]
After solving we get:
z = -1
y = 5
Plug the above two values in equation (1) we get:
x = 4
Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
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Can anyone help me solve this?
Answer:9
Step-by-step explanation:
Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]
We know both a and c, so it becomes
[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=
16+b^2=97=
97-16=b^2=
81=b^2=
9=b
Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
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My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
3. Twelve people work together: four of them are managers and eight of them are office workers. Two people are chosen at random from the twelve members of the group. Calculate the probability that one is a manager and one is an office worker.
Answer:
2/9
Step-by-step explanation:
8/12 you pick an office worker
4/12 chance you pick a manager
8/12 multiplied by 4/12 is 32/144
We can simplify this to 16/72
We can simplify this to 8/36
We can simplify this to 4/18
We can simplify this to 2/9
Solve each equation.
1. x+6=4
2.x- -4 = -6
3.2(x-1)=-200
4.2x+-3=-23
Step-by-step explanation:
1) x+6 =4
x. =4-6
x. =-2
2) x-(-4) =-6
x+ 4. =-6
x. =-6-4
x. =-10
3)2(x-1)=-200
2x-2 =-200
2x. = -200+2
2x. = -198
x. = -198/2
x. = -99
4)2x+(-3) =-23
2x-3. =-23
2x. =-23+3
2x. =-20
x. =-20/2
x. = -10
these box plots show daily low temperatures for a sample of days in two different towns which statment is the most appropriate comparison of the centers
The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°
What is the correct statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.
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f(x) = 5 + 4x2, then f(3) =
Step-by-step explanation:
To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².
That would look like this: f(3) = 5 + 4(3)²
f(3) = 5 + 4(3)²
f(3) = 5 + 36
f(5)=41
Therefore, the answer is 41.
I hope this helps!! :)
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction
Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
expression equivlant (x+5)^2
Answer:
(x+5) (x+5)
Step-by-step explanation:
it's just (x+5)^2 twice
Which of the following functions best models the data represented by the scatterplot shown below?
A: y=160x-100
B: y=2^x+12
C: y=8x^2+10
D: y=25x+20
Answer:
C: y = 8x^2 + 10.
Step-by-step explanation:
It looks close to being a parabola so I think it is probably a function in x^2.
Try 8x^2 + 10
Checking against the plot
When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200
Calculating y for other values:
When x = 7, y = 8(7)^2 + 10 = 402, and on graph y = 400.
When x = 11, y = 978 , and on graph = 1000.
When x = 17, y = 2322, and on graph y = about 2350.
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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2. Mikaela counted 2 more turtle nests
on a North Carolina beach than
Diego. If Mikaela counted 38 turtle
nests, which equation could you use
to find the number of turtle nests
Diego counted?
A 2x = 38
B x÷2=38
C x - 2 = 38
D x + 2 = 38
PLEASE HELPPP ITS WORTH 20 points!!!
Answer:
tanD =4/7
Step-by-step explanation:
tanD = P/B
Where P=4 and B=7
So;
tanD=4/7
Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.
Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.
What is the proof that ∠A ≅ ∠E?Looing at ΔOAB and ΔOEF
It is clear that
OB = OF (O is the midpoint)
∠OBA = ∠OFE = 90°
Therefore
∠AOB = ∠EOF (Vertically Opposite Angles)
⇒ ΔOAB ≅ ΔOEF and
∠ A ≅ ∠E.
QED
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There are two pieces of wires, each of length 66 cm. One wire is bent into a square and the other wire is bent into a circle. Find (a) the area of the square, (b) the area of the circle.
Answer:
Area of Circle = 346.5 cm².
Area of square = 272.25 cm ² .
Step-by-step explanation:
So , 2πR = 66
2 × 22 / 7 × R = 66
R comes out is 21/2 cm .
Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2
= 693 / 2 = 346.5 cm².
If bent into the shape of a square ;
4 a = 66
a = 33/2 . ( Side of a square )
Area of square = a ² = 33×33/4 = 1089/4
= 272.25 cm ² .
for each sequences, find the first 4 term and the 10th term the sequences are
(a) n^2+3
(b)2n^2
Answer:
see explanation
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule
to find the 10th term substitute n = 10 into the rule
(a)
a₁ = 1² + 3 = 1 + 3 = 4
a₂ = 2² + 3 = 4 + 3 = 7
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 3 = 16 + 3 = 19
a₁₀ = 10² + 3 = 100 + 3 = 103
(b)
a₁ = 2(1)² = 2(1) = 2
a₂ = 2(2)² = 2(4) = 8
a₃ = 2(3)² = 2(9) = 18
a₄ = 2(4)² = 2(16) = 32
a₁₀ = 2(10)² = 2(100) = 200
(x + 8/3)^2 + y^2 = 1 What is the center of the circle? what is the radius?
(x+8/3)²+y²=1
(x+8/3)²+y²+0²+2×0y=1
(x+8/3)²+(y+0)²=(V1)²
->center: C(8/3,0)
-> radius: V1
Mrs. Yamaguchi's class weighed the potatoes that they grew in their garden and recorded the data on a table. Determine how many dots are above each data value in a line plot of this data.
Weights of Potatoes (in pounds)
1
4
3
8
5
8
1
2
5
8
1
2
1
2
3
4
1
4
1
8
3
4
1
2
3
8
1
2
3
4
3
8
The value
1
8
will have
Choose...
dots above it.
The value
1
4
will have
Choose...
dots above it.
The value
3
8
will have
Choose...
dots above it.
The value
1
2
will have
Choose...
dots above it.
Using a dot plot, it is found that the number of dots of each point are given as follows:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.The value [tex]\frac{1}{4}[/tex] will have two dots above it.The value [tex]\frac{3}{8}[/tex] will have three dots above it.The value [tex]\frac{1}{2}[/tex] will have five dots above it.The value [tex]\frac{5}{8}[/tex] will have two dots above it.The value [tex]\frac{3}{4}[/tex] will have three dots above it.What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, one measure has a value of 1/8, hence:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.
Two measures have a value of 1/4, hence:
The value [tex]\frac{1}{4}[/tex] will have two dots above it.
Three measures have a value of 3/8, hence:
The value [tex]\frac{3}{8}[/tex] will have three dots above it.
Five measures have a value of 1/2, hence:
The value [tex]\frac{1}{2}[/tex] will have five dots above it.
Two measures have a value of 5/8, hence:
The value [tex]\frac{5}{8}[/tex] will have two dots above it.
Three measures have a value of 3/4, hence:
The value [tex]\frac{3}{4}[/tex] will have three dots above it.
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Answer:
1 2 3 5 2 3
Step-by-step explanation: